**2 人解决**，43 人已尝试。

**2 份提交通过**，共有 91 份提交。

**9.9** EMB 奖励。

**单点时限: **2.0 sec

**内存限制: **256 MB

Mom and dad have a problem: their child, Reza, never puts his toys away when he is finished playing with them. They gave Reza a rectangular box to put his toys in. Unfortunately, Reza is rebellious and obeys his parents by simply throwing his toys into the box. All the toys get mixed up, and it is impossible for Reza to find his favorite toys anymore.

Reza’s parents came up with the following idea. They put cardboard partitions into the box. Even if Reza keeps throwing his toys into the box, at least toys that get thrown into different partitions stay separate. The box looks like this from the top:

We want for each positive integer , such that there exists a partition with toys, determine how many partitions have , toys.

The input consists of a number of cases. The first line consists of six integers . The number of cardboards to form the partitions is () and the number of toys is given in (). The coordinates of the upper-left corner and the lower-right corner of the box are and , respectively. The following lines each consists of two integers , indicating that the ends of the th cardboard is at the coordinates and . You may assume that the cardboards do not intersect with each other. The next lines each consists of two integers specifying where the th toy has landed in the box. You may assume that no toy will land on a cardboard.

A line consisting of a single terminates the input.

For each box, first provide a header stating `Box`

on a line of its own. After that, there will be one line of output per count of toys in a partition. The value will be followed by a colon and a space, followed the number of partitions containing toys. Output will be sorted in ascending order of for each box.

Input

4 10 0 10 100 0 20 20 80 80 60 60 40 40 5 10 15 10 95 10 25 10 65 10 75 10 35 10 45 10 55 10 85 10 5 6 0 10 60 0 4 3 15 30 3 1 6 8 10 10 2 1 2 8 1 5 5 5 40 10 7 9 0

Output

Box 2: 5 Box 1: 4 2: 1

**2 人解决**，43 人已尝试。

**2 份提交通过**，共有 91 份提交。

**9.9** EMB 奖励。

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